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Coordinate Frames

A coordinate frame is a reference system consisting of an origin and a set of orthogonal axes used to define the position and orientation of points, vectors, or objects relative to that frame.

Attaching it to a point on a rigid body allows us to describe the world in terms of the body's local coordinate system. There are various frames like the world frame, the body frame, and the sensor frame.

In robotic manipulation, simulation, and computer graphics applications, multiple coordinate frames are organized in a hierarchical structure. For example, a sensor frame may be attached to a robot link frame, which is attached to the robot base frame, which is defined relative to the world frame.

Robotics primarily utilizes right-handed coordinate systems because they are consistent with the conventions used throughout mathematics, physics, and engineering. This consistency simplifies the application of concepts such as rotations, cross products, angular velocities, and rigid-body transformations, and promotes interoperability across disciplines and software systems.

Right Hand Coordinate System Example​

  • There is a coordinate frame with x, y, and z axes that follow the right-hand rule then let's say the thumb points towards z axis in positive direction, we have open hand towards x and then when we curl. Then we reach the y axis.

Robot Frame​

We will apply the following convention:

  • Origin (O) will the center of mass of the robot
  • The x-axis will point in the forward direction of the robot
  • The y-axis will point to the left of the robot
  • The z-axis will point upwards from the robot

Camera Frame​

We will apply the following convention:

  • Origin (O) will be center of the camera
  • The x-axis will point to the right of the camera
  • The y-axis will point downwards from the camera
  • The z-axis will point in the forward direction of the camera towards the scene

Image Frame​

We will apply the following convention, when looking at the image:

  • Origin (O) will be top-left corner of the image
  • The x-axis will point to the right of the image
  • The y-axis will point downwards from the image

Further Reading:​